Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

Table 2

Numerical results of Example 2 for 𝛼=1.

𝑡	Exact solution	Absolute error in [22]	Absolute error in [20]	LWM	LWM	LWM
				𝑀=2, 𝑘=2	𝑀=3, 𝑘=2	𝑀=5, 𝑘=3
0.1	0.110295	1.23𝐸−15	2.81𝐸−03	0	0	0
0.2	0.241976	5.24𝐸−15	3.83𝐸−04	0	0	0
0.3	0.395104	8.16𝐸−15	1.23𝐸−04	0	0	0
0.4	0.567812	1.15𝐸−12	2.86𝐸−03	1.68𝐸−12	1.66𝐸−15	1.43𝐸−16
0.5	0.756014	6.17𝐸−12	4.38𝐸−04	2.22𝐸−12	2.12𝐸−15	1.66𝐸−16
0.6	0.953566	4.55𝐸−11	5.19𝐸−02	1.15𝐸−12	1.10𝐸−15	1.54𝐸−16
0.7	1.152946	7.57𝐸−10	2.14𝐸−02	1.27𝐸−12	1.11𝐸−15	1.33𝐸−16
0.8	1.346363	6.33𝐸−09	1.42𝐸−02	1.87𝐸−12	2.01𝐸−15	1.75𝐸−16
0.9	1.526911	3.67𝐸−08	6.98𝐸−03	1.93𝐸−12	2.66𝐸−15	1.87𝐸−16
1.0	1.689498	1.64𝐸−07	4.96𝐸−03	1.56𝐸−12	1.66𝐸−15	1.64𝐸−16